Use ruler and compasses only for this question. Draw a circle of radius $4 \mathrm{cm}$ and mark two chords $\mathrm{AB}$ and $\mathrm{AC}$ of the circle of length $6 \mathrm{cm}$ and $5 \mathrm{cm}$ respectively.
Construct the locus of points, inside the circle, that are equidistant from $\mathrm{A}$ and $\mathrm{C}$. Prove your construction.
 

Use ruler and compasses only for this question. Draw a circle of radius $4 \mathrm{cm}$ and mark two chords $\mathrm{AB}$ and $\mathrm{AC}$ of the circle of length $6 \mathrm{cm}$ and $5 \mathrm{cm}$ respectively.
Construct the locus of points, inside the circle, that are equidistant from $\mathrm{AB}$ and $\mathrm{AC}$.

Draw a line segment $AB$ of length $12 \mathrm{cm}$. Mark $M$, the mid-point of $AB$. Draw and describe the locus of a point which is at a distance of $3 \mathrm{cm}$ from $AB$.

Draw a line segment $AB$ of length $12 \mathrm{cm}$. Mark $M$, the mid-point of $AB$. Draw and describe the locus of a point which is at a distance of $5 \mathrm{cm}$ from the point $M$.